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Questions and Answers
What is the characteristic of diamagnetic materials when a magnetic field is applied?
According to Curie's law, what is the relationship between the magnetization M of a paramagnetic sample and the external magnetic field Bext?
What is the effect of increasing temperature T on the magnetization M of a paramagnetic sample?
What is the reason for the persistent alignment of magnetic dipole moments in ferromagnetic materials?
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What happens to the magnetic dipole moments of diamagnetic materials when the external magnetic field is removed?
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What is the term for the ratio of the magnetic dipole moment to the volume V of a sample?
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Which type of material exhibits permanent magnetism due to the alignment of magnetic dipole moments?
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What is the effect of increasing the external magnetic field Bext on the magnetization M of a paramagnetic sample, according to Curie's law?
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What is the condition for Curie's law to be valid?
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What is the result of exchange coupling in ferromagnetic materials?
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Study Notes
Maxwell's Equations and Magnetism
- Gauss's Law for Magnetic Fields: The net magnetic flux through any closed Gaussian surface is zero, where B is the magnetic field.
- The law holds even if the Gaussian surface does not enclose the entire structure.
- A magnetic dipole is enclosed by a Gaussian surface, and the net flux through the surface is zero.
Induced Magnetic Fields
- The magnetic field induced along a closed loop by a changing electric flux FE in the region encircled by that loop.
- The magnetic field induced by a changing electric field is shown at four points on a circle with a radius less than the plate radius.
- Ampere-Maxwell Law: ∇ × B = μ₀(ienc + ε₀∂E/∂t), where ienc is the current encircled by the closed loop.
Displacement Current
- The product of the electric field and the area of the plates of a parallel plate capacitor has the dimension of a current.
- The displacement current id is a fictitious current that is encircled by the integration loop.
- The magnetic field induced by a changing electric field is related to the displacement current.
Maxwell's Equations
- A set of equations that describe the relationships between electric and magnetic fields.
Magnetism of Earth
- Earth's magnetic field is that of a magnetic dipole, with a magnetic dipole moment m.
- The field declination is the angle between geographic north and the horizontal component of the field.
- The field inclination is the angle between a horizontal plane and the field's direction.
Magnetism and Electrons
- An electron has an intrinsic angular momentum called its spin angular momentum, and an intrinsic spin magnetic dipole moment.
- The orientation energy for the electron in an external magnetic field is related to its spin magnetic dipole moment.
- An electron in an atom has an orbital magnetic dipole moment, which is related to its orbital angular momentum.
- The orientation energy is quantized, with only certain components allowed.
Magnetic Materials
- Each electron in an atom has an orbital and spin magnetic dipole moment, which combines to produce a magnetic field in a material.
- There are three general types of magnetism: diamagnetism, paramagnetism, and ferromagnetism.
- Diamagnetism: Weak magnetic dipole moments are produced in the atoms of a material when it is placed in an external magnetic field.
- Paramagnetism: Each atom has a permanent resultant magnetic dipole moment, but the moments are randomly oriented, and the material lacks a net magnetic field.
- Ferromagnetism: Some electrons have their resultant magnetic dipole moments aligned, producing regions with strong magnetic dipole moments.
Diamagnetism
- A diamagnetic material develops a magnetic dipole moment and experiences a magnetic force when a magnetic field is applied.
- When the field is removed, both the dipole moment and the force disappear.
Paramagnetism
- The magnetization M of a paramagnetic sample is directly proportional to the magnitude of the external magnetic field and inversely proportional to the temperature.
- Curie's Law: M = CBext/T, where C is the Curie constant.
Ferromagnetism
- Exchange coupling is a quantum physical effect that causes alignment of the magnetic dipole moments of atoms in ferromagnetic materials.
- This alignment is what gives ferromagnetic materials their permanent magnetism.
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Description
Quiz on Maxwell's Equations, Gauss's Law for Magnetic Particles, and Magnetism of Matter, covering concepts like magnetic fields and Gaussian surfaces.
